Yes, that's exactly why it is 3 and not 4. It is sin(a) you want, not .

Compare
and . You should see immediately that you want to have Rsin(a)= 3 and Rcos(a)= 4. Set the coefficients of and in the two equations equal.

So in this one: you put a/b (3/4) not b/a (4/3) because sin (a) comes before cos (a)? So the method for doing these questions is to take the general formula of and swap it around like you have and take it that way?

So in this one: you put a/b (3/4) not b/a (4/3) because sin (a) comes before cos (a)? So the method for doing these questions is to take the general formula of and swap it around like you have and take it that way?

Don't overthink this.

You have essentially said at the beginning of the question (correctly):

Let

In order for both sides of the equation to be equal, both sides have to have